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The International Summer School-Conference “Advanced Problems in Mechanics — 2021” is the forty eighth in a series of annual summer schools held by Russian Academy of Sciences. The Conference is organized by Peter the Great St.Petersburg Polytechnic University (SPbPU) and Institute for Problems in Mechanical Engineering of Russian Academy of Sciences (IPME RAS) under the patronage of Russian Academy of Sciences (RAS). APM 2021 is partially su¬pported by Russian Foundation for Basic Research and Academic Excellence Project 5-100 proposed by Peter the Great St. Petersburg Polytechnic University. The main purpose of the meeting is to gather specialists from different branches of mechanics to provide a platform for cross-fertilisation of ideas. The list of problems under investigation is not limited to questions of mechanical engineering, but includes practically all advanced problems in mechanics, which is reflected in the name of the conference. The main attention is given to problems on the boundary between mechanics and other research areas, which stimulates the investigation in such domains as micro- and nanomechanics, material science, physics of solid states, molecular physics, astrophysics and many others. The conference “Advanced Problems in Mechanics” helps us to maintain the existing contacts and to establish new ones between foreign and Russian scientists.